Wales online.
What is for certain, is Grimes has played his last game for the Swans, having made 333 appearances for the club over the last 10 years.
"A deal has been agreed, and the terms have been agreed," WIlliams said ahead of this weekend's clash with Frank Lampard's men. "So now it's just the matter of some official paperwork to be signed and sent back and forth to complete that transaction.
"We're sorry to see Matt leave us. He's been an incredible servant to the club. Incredible record in terms of the number of minutes he's played on the pitch and the level he's played at. But we move on.
"Having worked in football for a number of years I tend to be less surprised at things. That's the nature of the business we work in. It's extremely competitive and it's a jungle.
"So I was a bit shocked initially. But, of course, you have to move on very quickly."
Grimes stands to earn a hefty increase on his current wage package once he completes his move to the CBS Arena, with Coventry set to make the midfielder one of their top earners.
Williams says tentative conversations were held over a possible counter offer to keep him at the club. But it soon became clear that they were not going to be able to compete with the terms Coventry could offer.
"We spoke," he added. "I picked the guy for every game, and I think I only ever brought him off once because he's incredible.
"But we couldn't agree anything here and he decided another option was better for him and we were not able to convince him.
"I'm not in the correct position to talk about all of the reasons, and there are many I'm sure. If it was as simple that he wanted to play for one team or another, then that would be hurtful.
"But the reasons are more than that and it's disrespectful for me to talk about all the things that are potentially involved in his decision to move."
The value of the deal taking Grimes to the Sky Blues is understood to be between £3.5m and £4m, a valuation Williams feels represents good value for all involved.
"It's extremely good business all round. It's a very good deal for us. It's fantastic for them because he's a great player. So it's a fair deal all round."
Attention will now turn to the transfer market - and possible replacements. But it seems there has already been a decision made on who will replace Grimes as captain.
“We have Ben Cabango who will step up into the role of captain," Williams confirmed. "He is a player who has captained the club at every level he has played at, and has come through the academy.
“He is very much someone in the mould of a leader and it is his time to shine now and we move forward.
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